I looked into this a couple of years ago, as one of my clients is a heavy user of ASP and I was required to develop a new site and application for them.
It is possible to run ASP on Apache, but y understanding is that it is not recommended. There are many caveats, and you may be frustrated by the differences between ASP on a Windows server versus ASP on a Unix server.
If you're not too far into development, you might consider using a more portable platform such as PHP rather than ASP, as PHP sites can run on either Unix servers or Windows servers.
If you already have a lot of work invested in ASP, then you may prefer to remain with APS. In that case, check with Matt about when WHB will launch its Windows hosting plans.
I am not WHB staff and I am not paid.
I provide help in these forums on my own time.