The Oregon Ducks are currently just a few very winnable basketball games from going undefeated at home this year in football and both men’s and women’s basketball; their aggregate home record is currently 39-0.
Has any school ever done this before?
Wild guess maybe Connecticut?
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Undefeated in football is fairly common, but I’ve never heard of undefeated in basketball. Men’s and women’s basketball, and football at the same time, would I expect be unprecedented.
Does it count considering that football season was technically last year?
They’ve not been a particularly strong football program in recent decades (i.e., when the basketball teams have been good), and looking at Wikipedia, it appears that the only season they’ve had where the football team was undefeated may have been 1924, when they were 6-0-2.
I’d say it’s all in the same academic year, so I’d count it.
Note the question is about going undefeated at home. It’s still quite an accomplishment, but not quite the same as undefeated overall.
Ahh, thank you for the clarification. That makes it a bit harder to research. 
ESPN has each Division I school’s home records in those three sports going back to 2003.
It’s probably going to be really hard to get information on women’s basketball before the NCAA started running it in, IIRC, 1981 (certainly by 1982).
There have been 7 men’s basketball teams in the NCAA era who have gone undefeated; most of them were by UCLA’s dominant teams in the 60’s and 70’s (thanks, Bill Walton and Lew Alcindor), it includes a San Francisco team with Bill Russell in the paint, and the last was Bobby Knight’s Indiana Hoosiers in 1976.
Misread the question thought it was Mens and Womens basketball only.
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In division 3 UW Platteville went undefeated in men’s basketball (under Bo Ryan). No idea on the women’s team.
Brian
Cornell Men’s and Women’s hockey teams just finished their regular seasons with undefeated home records. A combined 27-0-3.
Going off ESPN’s site:
Austin Peay was undefeated at home in 2002-03 in both basketballs, but not football.
Iowa, Ohio State (x2), BYU, Wisconsin have all been undefeated at home in MBB and Football, but not WBB.
There are like 6-7 basketball teams that go undefeated at home every year, it’s not terribly uncommon. Kansas, Duke, Kentucky, Gonzaga, Ohio State, Illinois, Arizona, and others have all done it multiple times in recent memory.
Oregon men’s BB won their final home game last night, so the hypothetical is now true.