If these are completely different functional applications with no shared data between them, then no, I would not put them into the same database. The sizes you're talking about are fairly small, so taking a 10gb database and making it 15gb is pretty trivial, so I wouldn't argue from that stand point. Instead, I'd worry about the fact that deployments to one application will affect the up-time and availability of the other. I'd worry about the fact that you've got users in the database that shouldn't have access to other apps, so now you have to get security set up differently within each database. As a general rule of thumb, if they're not sharing data, don't put them into the same database.

Just a thought, is your boss an Oracle person? They refer to a database what would, on the SQL Server side, be basically an instance. So they think they need to jam everything into one db when they don't.