Zorro,
Sharing a Forms Based Authentication (FBA) authorization cookie would be one of the cheaper and easier routes to investigate/implement, but you've indicated that FBA isn't an option for you. That said ...
... without knowing more about the custom authentication mechanism you have in place on your ASP.NET application, it's very difficult to offer a good suggestion. CptSkippy's question (regarding reconciliation) is a good one, as that becomes the basis for what's feasible and what isn't. If your app and site don't share a common user base, then SSO becomes a real challenge.
I don't know how feasible it is for you and your situation, but Microsoft's ISA 2006 server does an admirable job when used in an SSO role. It supports a wide variety of publishing and authentication mechanisms, and it plays quite nicely with SharePoint leveraging both NTLM and Kerberos authentication:
http://technet.microsoft.com/en-us/library/bb794722.aspx
The big question, again, is your custom ASP.NET application. If you've got some flexibility there, ISA may be a option.
For what it's worth!