My boyfriend and I have been together for almost 2 years. When he was 19 he was pulled over and had a BAC of less than .08 (the legal limit here), but because he was underaged he was charged with a DUI. Last June he was pulled over for speeding in the state of Wisconsin and the officer asked to search his car. He found a smoking device and a small bag of marijuana in the car, so his blood was taken and came up positive for THC (even though he hadn't smoked for somewhere between 12-24 hours) . He was charged with a DUI, possession, and possession of paraphernalia.
Needless to say, he no longer smokes pot. It is just too risky now.

Will these charges be enough that we are not able to rent an apartment from a place where they do background checks? Or are those mostly searching for violent crimes and felonies?

Please answer my question and do not give me your opinion on my boyfriend or my relationship. That is not what I am asking for and it is quite annoying when people do that.
I wish I could rent in my name, but he is graduating college in April and will be the one working full time & making a much better hourly wage than I am. I am still attending college full time & only work at a bagel shop on weekends. I'd like to get my masters so I will have at least 4 more years left in school, maybe 5 or 6, and if we can't rent an apartment on his income we won't be able to move out until I graduate.