If you live in a community property state and the home was acquired during the marriage, the property's entire basis is stepped up when a spouse dies. In other words, the cost basis of the home would be the fair market value at the time of the spouse's death.
If you do not live in a community property state, the cost basis is increased by half the property's value at the time of your spouse's death.
For example, if you originally bought the home for $200,000, half of your cost basis is $100,000. If the house's value was $300,000 at the time of your spouse's death, you would add half that value ($150,000) to your half of the original cost basis which would result in a new cost basis of $250,000 ($100,000 plus $150,000) that you would use upon selling the home.
Any improvements made to the home before your spouse's death would be added to the original cost basis. Any improvements made to the home after your spouse's death would be added to your new cost basis.
For example, let's assume you made $10,000 in home improvements before your spouse's death. The cost basis in your home would then be $210,000 in the above example. You would then take half of that amount ($105,000) and add half the value of the home at the time of death to calculate your new cost basis of $255,000 ($105,000 plus $150,000). Any improvements made after your spouse's death would be added to your new cost basis for the full amount of the improvement.
