I know the particular application of BSA & Milk. But, my query, why many laboratories follow the combination of BSA+Milk as a blocking reagent? And, how they get advantages from this combination?
BSA as a single, well defined protein is not too good at blocking non-specific sites. Dry non-fat milk powder is a mixture of proteins and usually does an excellent job, especially in combination with a mild detergent like Tween. Another good blocking agent is fish skin gelatin (not the bovine gelatin known from the kitchen, which is useless as blocking agent) , which compared to NFM has the advantage of giving clear solutions. In the end, selection of blocking agent is a matter of trial and error.
A combination of both does not make much sense. I use 5-10% milk for most antibodies. I just use 5 % BSA for the ones which react with milk (most of them being phospho-antibodies). I have never heard of a combination of blocking buffer with milk AND BSA. Maybe you mean that you use BSA with the 1st ab and milk with the 2nd? that is possible and makes sense, since just the 1st antibodies can react with milk.