To use a Mass Spectrometer to characterize a polymer does NOT make any sense. As the whole concept of mass spectrometry is to break up organic molecules into small ionized pieces which you get Mw peaks of each part and you put the parts together. Polymers will char, crosslink, and fall apart in odd ways in the furnace, and gum up the apparatus.

Use FTIR, GPC, DSC, and DTA and other methods to characterize polymers. A composite material is worse, as it is a mixture, not just including fiberglass but other ingredients as well.

Analysing a composite based compound with MS is an unnecessary analysis. Because MS break up the connection and bonds between the components and just you will be faced with alot of fractions peak.

As douglass said you must use the famous characterization methods like FTIR for investigating the chemical structure of composite, GPC in which analyze sample based on their molecular size and finally DTA and DSC in which thermal transition of the composite shows up. Also u can surface characterization by SEM and elemental analysis by EDX and so on.

I would definitely try MS techniques with minimal fragmentation, that is, electrospray ionization mass spectrometry (ESI-MS) if you find a suitable solvent. If not, try matrix-assisted laser desorption with time-of-flight detection (MALDI-TOF). Both methods are popular to analyse e.g. proteins where minimal (or no) fragmentation is a must.