I have two Health Insurance Policies of TATA AIG & Birla Sunlife. Will the expenses of Hpospitalisation be reimbursed by both the Insurers?

Yes and no. There is a rule called Coordination of Benefits when covered under two policies. One of the policies is listed as primary the other secondary. The primary policy pays first up to the limits of the policy. If the full amount isn't covered, you can submit a claim to the secondary for the balance.

Everything Scott said is correct and I will add that this is done to prevent overpayment back to you. So, essentially the 2nd policy is picking up the slack of the 1st policy. You won't receive any excess for having 2 policies.