My husband is a resident alien of the US and I am a US citizen. His mother recently died and his Dad sold the house. The money for the house will be given to my husband as inheritance because that was his mother's wishes. There will already be a decrease in the amount due to the exchange rate between the countries. Will the remaining amount that he brings into the US be taxes also?

In the U.S. there is no tax on inheritances. Since the money is coming from a foreign country you may be required to file Form 3520.

In addition to the above information, if the money is physically brought into this country, or physically shipped, and it exceeds $10,000 at a one time transaction, a form FinCen 105 needs to be completed. If it is however transferred using normal banking procedures like a wire transfer, the form does not need to be completed.