So firstly while Republicans are almost certain to retain the House, the Democrats may win back the Senate in 2016.
The answer to your question is fairly simple–we don’t know what Sanders will do because he essentially refuses to talk about the other important issues of the Presidency. In fact, most of his proposals are legislative, and 100% of the proposals he is willing to talk about at length are legislative. He answers foreign policy questions with vague statements and then switches back to his single issue. He answers racial justice questions with vague statements then segues into his single issue. Sanders is a progressive political movement masquerading as a Presidential candidate.
So getting that out of the way–despite his not talking about it much, we can infer Sanders will probably favor a fairly isolationist foreign policy. I cannot imagine he would commit to any sort of fight against ISIS or NATO build up in the east to try and face down Russian ambitions. He will likely ignore North Korea’s bellicose actions and is likely to essentially abandon our Pacific allies. I can only assume that a man who has voted against any fairly broad-based (both at home and in the international community) use of force (like Gulf War I, which had overwhelming support and was backed by an actual UN Resolution) he will be the most non-involved President in history in terms of military foreign policy.
Hillary will likely continue Obama’s approach but maybe a little “sterner.” I don’t believe Hillary is going to get us involved in an Iraq/Afghan war sized conflict again, but she’ll use special forces and aerial attacks as she deems necessary against entities like ISIS. HRC is likely to extend the current 10,000 soldiers in Afghanistan who are suspected to be kept there into the next Presidency into an indefinite presence. While it’s technically scheduled they be gone by the end of Obama’s Presidency top brass are saying it’s not a good idea, and even Obama has been mum on it lately, and a lot of “Pentagon” watches think it may not happen.
If you’re more isolationist, then Bernie’s foreign policy will probably suit you just fine. Both HRC and Bernie are likely to preserve Obamacare (due to inability to pass anything to replace or improve it), and both will get decently liberal SCOTUS justices on the court, particularly if the Democrats do in fact win back the Senate.
Bernie is anti-trade, and it’s possible he can do things unilaterally to torpedo trade agreements–but trade agreements already in force he has little real ability to alter. Once a treaty has been ratified by the Senate it’s binding and the President won’t be able to unilaterally back out of it.
There’s a possibility that Sanders will attempt to use executive orders and other ‘creative potentially extra-legal’ actions to break up big banks. This will result in the majority of his Presidency being consumed by long, expensive, and potentially unwinnable lawsuits against the big banks (who aren’t going to go gentle into that good night.)