NimbostratusASM can only handle HTTP at this time, with some sensible fallback behaviours for Websockets. I've tried to look for and take a quick look at the PeSIT protocol specs but can't find any document suitable for quick skimming.
You can generally offload the SSL on bigip, because SSL is standardized, but the HTTP Profile which is required by ASM will choke if it receives non HTTP traffic.
Since you mentioned HTTPS as opposed to SSL, are you guys encapsulating the protocol over HTTP? or did you just mean SSL when you said HTTPS? If you encapsulate the protocol in HTTP, then you may be able to get somewhere with using ASM, provided the encapsulation can be broken down into standard http stuff, like predictable URLs, parameters, and parameter values.
