Check with your accountant, but yes you will get a step-up basis to the value on date of death of the decedent’s half. And if you sell within a few months, there should be no gains to report on that part. (If you’re not going to sell immediately, you should get a written appraisal of the value of the entire house closely after the date of death, so you’ll have a new “cost basis for that half.)
Your half will be treated as a capital gain — and there may be some impact from depreciation if you claimed that (thus see the accountant). But if it was just a simple co-ownership, your half will carry the cost basis on the date you became a co-owner. And if it was over a year, then you would get long-term capital gains treatment.
You obviously know that you don’t get the $250,000 homeowner’s profit exemption since it was not your residence.