I'm taking 30 mg of lexapro, 60 mg of Buspar (buspirone) and 50 mg of doxepin a day. I'm still experiencing anxiety and insomnia. Is this normal?

Are you relying on. Meds alone? If yes, then strongly recommend that you add in non-med therapies. Talking therapy ranks really high. Cognitive behavioral therapy can be quite effective. Aim for daily exercise, 8 hours of sleep per night ; good nutrition with 5 servings of veggies ; 4 of fruit per day. Try tai chi, yoga, qi gong, progressive muscle relaxation, deep breathing exercises ; meditation. Don't isolate.