Send email as alias

I’m a .net developer so I’ve got some experience of using code to send email, but I’m certainly no smtp/email guru. The business problem is that our staff need to send emails from another company’s (more than one company so looking for general guidance) email.
I know .net has the ability to put a ‘From’ different from the actual ‘From’ but it does get instantly flagged by all junk filters as (understandably) very potentially dodgy.
Obviously, the less I interact with someone else’s email sub-system the better (so I don’t get blamed when it breaks), but what is the usual way of doing this?
I know it’s a very sensitive security issue as it could cause havoc if done maliciously, but I was wondering what approach other people had taken.