You're still secure if you use https. If neither your computer nor the host you're connecting to has been tampered with, then you're safe irrespective of what's happening between.
While that used to be true, based upon recent history we, unfortunately, can't blindly trust HTTPS to always be "secure" 100% of the time anymore -- whether due to things like Heartbleed, fake certs signed by a root CA, protocol attacks, or some other vulnerability that hasn't even been discovered yet.