The first thing that came to mind when I thought of LGBT entertainment was "Husbands, the Series”. I hope it’s okay to link to a commercial venture – I’m not involved in it other than being a fan.
"Husbands" is about a couple who goes to Las Vegas, gets plastered, and wakes up the next morning, hungover and married. But the couple in question are two men who have been dating for a short time, and who went to Vegas to celebrate marriage equality becoming law in the US (so it’s set in what I hope is the very near future).
The first season is made up of eleven tiny episodes, written by JaneEspenson (BTVS, Dollhouse, Caprica, Torchwood) and Brad Bell, whom you may know as Cheeks. The cast and crew are white-hot bundles of talent.
I cannot recommend "Husbands" highly enough. Each 2-3 minute episode will make you laugh, break your heart, maybe make you cry, then make you laugh again. The only thing I don’t like about it is that I want more, more, more!
But they are filming a second season, yay! So there *will* be more Husbandy goodness coming soon. In the meantime, you can watch the first season, and here’s the first episode, to get you started: