For what reason do you not want to just use a single server side technology? If you have to ask this question than you probably don’t need to use both. Pick one or the other.
Rather than ask if it’s possible and how, pros vs. cons, products and links -
you will be able to get more helpful replies if you explain what you have in mind to do.
What kind of application?
What language is it written in?
In what ways do you hope using two different languages in the application would be beneficial?
It would make more sense to build an API in .NET or PHP than use a JavaScript framework client-side for the UI. You can do the same thing with .NET and/or PHP but it really doesn’t make all that much sense these days. That is unless there is an existing service in .NET and/or PHP of which you have no access to except through an API. Than you can use any language to interact with the existing service. I’m working on a project right now that is split between .NET (API/datastore) and PHP (application) but it isn’t very ideal.