Congrats and glad it with smoothly for you! I remember coming out to my parents and it was much the same with my mother. It was kind of funny because her response was on the lines of "I already know." My dad on the other hand ... he kept insisting that I just hadn't found the right girl. His next question was "What do you look for in a guy that is so different?" My response to him was "Don't worry dad, it's not you!"
This got a few chuckles, but for the next 8-12 months, he always insisted I just needed to find the right girl and I would be happy. Finally that stopped, he met my boyfriend, now fiance, and while he didn't say it in person, he did approve and was glad I am finally genuinely happy.