If your H1B is expiring soon, lets say you have just 3 months of H1B before it expires, then it's not a good idea to use H1B to visit Nepal provided you entered US in F1 status. That means, when you try to enter Nepal, your visa status has changed from previous F1 to H1B , then you need to stamp visa again from Embassy. Lots of people prefer going to Canada or Mexico for stamping before going to Nepal. Some prefer going to Nepal for restamping. We discuss about this stamping issue in previous threads lots of times with Pros and Cons.

I would suggest not to use H1B if its validity is less than 6 months, and if you use your TPS travel document , that will be safe to return back to US. I do not think your H1B visa will be invalid. Better consult with Nepali lawyer to be on the safer side anyway.

Contact Nepali lawyer:

Bandita Sharma Dahal, VA
Khagendra GC, NY
Binod Rokka, NY
Dilli Raj Bhatt, NY
Keshab Raj Seadie, NY
Bashu Dev Phulara,NY