DH, on the internet, is a jokey-kind short form of darling husband. People use it to talk about their husband without writing the word husband every time: 'DH is watching the kids,' 'DH made dinner.' It grew on British parenting and women's forums and then spread. It is casual, in-group writing, not something you say out loud in a meeting, and not how you would write in a school essay. The tone is usually fond, sometimes eye-rolling, the way family nicknames are. Other letters work the same way on those forums: DD darling daughter, DS darling son, DH darling husband. This DH is not the baseball DH (designated hitter) and not Department of Health; those are different jobs for the same two letters.