As others have already, there is Mono, but given it's immaturity, it is not only an extra level of complexity, it is an extra level of risk. Furthermore, the supplier offering a .NET solution is highly unlikely to want to support their application on Apaches + Mono.
So either opt for OSS (Apache + PHP/Perl/Python/Ruby etc) or choose IIS + .NET. There is absolutely nothing wrong with choosing the .NET solution, if it's the best application for the job, but don't try to shoe an application essentially designed for one platform onto another.