This type of  association can be attributed to Bimodal volcanism, i.e.,  eruption of both mafic and felsic lavas from a single volcanic centre with little or no lavas of intermediate composition. This type of volcanism is normally associated with areas of extensional tectonics, particularly rifts.

Most occurrences of bimodal volcanism are associated with thinning of the crust and the presence of such rocks in metamorphic sequences has been used to provide evidence for past rifting events.

As pointed out by Assori, this observation is often associated with continental rifts (but not always the case) and in places where excess mantle-derived magmatism ("hot-spot") interacts with continental crust. The latter may or may not be associated with large amounts of stretching.

Some good examples of magmatism in continental rifts are some areas of the Basin and Range province in the western US, and regions of the East African rift/Afar Depression.

The idea is that the bimodal nature of the magmatism is due to large volumes of mantle-derived basalt intruding the crust and errupting at the surface. Simultaneously some basalt "ponds" in the lower crust resulting in crustal melting and assimilation to produce the silicic magmas, some of which erupt to the surface as rhyolite or peralkine silicic lavas.

Here are some good papers:

http://ir.library.oregonstate.edu/xmlui/bitstream/handle/1957/46864/FordMarkCEOASBimodalVolcanism.pdf?sequence=1

http://gsabulletin.gsapubs.org/content/94/8/1005.abstract 

http://www.nature.com/articles/ncomms5199

Dear Damepaia: not much to add the the previous answers, only the historical fact that decades ago the bimodal basalt-rhyolite association was considered as formed by liquid inmiscibility differentiation processes in basaltic magma, a phenomenon seen in the glass of Mare Tranquilitatis basalts in the Moon. However, this process cannot explain the enormous volume of extruded rhyolites, so a better explanation should be found. More recent isotopic evidence shows that the basalt is, of course, of mantle provenance, and has very low (87Sr/86Sr)0, but the rhyolites are of continental provenance, as a product of partial fusion of "granitic" material (actually granulitic) in the base of the continental crust, and hence show higher values of (87Sr/86Sr)0. This bimodal suite is characteristic of rift valleys, hot spots (Yellowstone) in basalt plateaus (Deccan, Paraná, Karroo, Columbia, Etiopía, and Siberian Trapps, among others), and also of the initial stages of back-arc spreading, especially if this happens in continental crust, behind an active margin. Regards, Sebastian. 

Dear Mamepaia,

You have some high quality information in the comments of Asoori, Alexandro and Sebastian, and there is no point repeating it.

But it so happens that early this morning I submitted a paper for publication in which there is a brief reference to bimodal mafic-felsic magmatism. Our paper concerns Nagar Parkar area in SE Pakistan , where the rocks of the Malani LIP extend.     Here are three references, the first two on Malani Igneous Suite and the last on Death Valley. In agreement with the three experts, we think that our bimodal magmatism also resulted from partial melting of the crust by ponded mafic magma.

Kochhar N, Dhar S, Sharma R (1995) Geochemistry and tectonic significance of acid and basic dykes associated with Jalor magmatism, west Rajasthan. Geol Soc India, Mem 33: 375–389.  

Singh LG, Vallinayagam G (2012) Petrological and geochemical constraints in the origin and mineralization of A-type granite suite of the Dhiran area, northwestern peninsular India. Geoscience 2: 66–80.

Smith EI, Tibbetts A, Belmontes H, Johnsen R, Walker JD (2016) Pliocene basaltic and rhyolitic volcanism in the Greenwater Range, Death Valley area, California. In: Proceedings, Natural History Conference, Death Valley Natural History Association, 3–43. https://www.researchgate.net/publication/285234149.

Regards,

Qasim

Article Pliocene Basaltic and Rhyolitic Volcanism in the Greenwater ...

You have good answers, especially those of from Alexandros Kostantinou and Sebastian Grande. I can give you some examples in the western USA, where continental bimodal magmatism associated with the Rio Grande rift and the Yellowstone hot-spot track. In both of these examples, most felsic magmatism preceded voluminous mafic magmatism— possibly because mafic magma collected beneath, heated, and partially melted deep continental crust before the rift was structurally open-enough, or before the mantle plume provided enough thermal energy to allow mantle-derived mafic magmas rapid upward movement through the continental crust. 

In the Mesoproterozoic Belt-Purcell basin, however, voluminous mafic sills intruded at about 1379 Ma, before large A-type granite plutons (with minor comagmatic mafic inclusions and hybrid diorite) intruded from about 1378 to 1350 Ma. Similarly, in the Challis volcanic field (in the back-arc region of the Cordilleran orogen), basaltic to andesitic strato-volcanoes preceded felsic calderas. 

As noted by Sebastian Grande, Sr- and Nd- isotopic initial ratios, can test whether your felsic magmas represent partial melts of older continental rocks, or whether they were derived from mafic parent magmas (by either fractional crystallization or imiscibility). 

I don't know how to test for immiscible mafic and felsic magmas, unless you could find felsic melt inclusions in your mafic rocks, or mafic melt inclusions in your felsic rocks, or both. In hybrid rocks I have seen, mafic inclusions in felsic rocks have chilled margins, and felsic inclusions in mafic rocks appear altered and partially resorbed (or melted).

Another approach would be to get full chemical analyses of samples of mafic and felsic rocks, and use the data to make chondrite-normalized spidergrams for incompatible and immobile trace elements. Compare those to published spidergrams for mafic and felsic rocks from known tectonic settings. The following article would be a good introduction.

Thompson, R.N., Morrison, M.A., Hendry, G.L., and Parry, S.J., 1984, An assessment of the relative rolls of crust and mantle in magma genesis: an elemental approach: Philosophical Transactions of the Royal Society of London, ser. A., v. 310, p. 459-590, doi:10.1098/rsta.1984.0008. 

Best regards, and good luck with your project.

Dear Damepaia: Here I adjoin two spectacular photos of a Late Tertiary bimodal association which I took in 2005 at Big Bend National Park, in southern Texas. Bright white, subhorizontal rhyolite tuffs are intruded by blackish basalt plugs. I hope you enjoy them! This volcanic region is located in the southern part of the Rio Grande Rift, near the Mexican border. Regards, Sebastian.