Is it healthy to be on antibiotics for 3 months.?

That depends: There are medical conditions that require long term antibiotic therapy. If you are having recurrent infections of any kind, that is something to have investigated by a doctor. Long term use can cause side effects like diarrhea, yeast infections and others. Generally i would only think of it as unhealthy if the use of such antibiotics was not medically appropriate.

Normally not but: Normally it is not healthy as it can cause complications like diarrhea and others But some infection you have to take antibiotics for three months or more like Lyme Disease,Osteomylitis,Tuberculosis,AIDS and few other as it is medically necessary

Depends: It depends why someone is on long term antibiotics. In some cases like recurrent urine infection, acne etc long term antibiotics are required .