Could the other person use the internet?
Phone patch:
Some repeaters have a telephone interconnection that can allow placing a telephone call from your radio.
Used to be pretty popular back before everyone had a cell phone. Now, not so much.
It's pretty limited, though.
Voice to Voice:
Not possible unless the non-licensed person has a licensed person sitting next to them.
APRS:
APRS has a way to do some rudimentary text messaging, but probably not what you are looking for.
Packet radio:
Can do simple e-mail type functions.
For voice to voice, there really isn't any legal way to do what you want.
Most amateur radios cannot do anything (legally) other than transmit on amateur radio frequencies. Some radios can be set up to work on MURS, GMRS, Land Mobile radio, etc. I think you have a Yaesu FT-7900, and that can only TX (legally) on amateur radio frequencies.
This is one of the reasons why GMRS is a valid option for some people. With GMRS, your GMRS license would cover your family.
---amateur radio licenses (all levels) have ZERO privileges on GMRS---
You would need your own GMRS license for your family in addition to a suitable radio to work on GMRS.
Getting others to get their amateur radio license can be a real challenge.