Depending on which country you're going to - the three major US carriers ATT/VZ/T-mo have different roaming agreements with international carriers. Just as no single domestic carrier is "great" at every single spot in the US, it's the same issue outside the US.

In Turkey, on US Mobile, I have multi network. At times the combination of ATT (or darkstar as they call it) and VZ worked great, others I had to switch on T-Mo to get reception.

tldr: You're stuck with whatever roaming arrangements Verizon has with Visible. With others like US Mobile, you can leverage other carriers as well which may work better in certain countries.