Clayton,
An 80watt panel is likely to give you around 6.5 amps under full sun, so
plenty to run fridge(1.5 amps average load?) as well as top the battery up.
I wouldnt charge the battery without the fridge connected, though, as 6.5
amps is getting a bit high for anything smaller than around a 140amp/hr
battery.
If the panel is likely to be connected for a long period of
time(weeks/months), you would have to get your charge rate to no more than
the magical figure of 1/21 of the lead/acid battery amp/hr rating(roughly
5.2 amps for a 110amp/hr battery). However, if we are talking for a few
days or even a week, you would be close enough to this figure to not have
any worries, and the fridge will be sucking some of this.
Battery technology is about the biggest limiting factor in making use of
the sun for power; the new battery technologies soon to hit the market seem
to be comfortable with massive charge rates, which opens the door for
oversized panels that can charge the battery in a short period of time.
Unfortunately, the most affordable battery tech (lead/acid) is also about
the slowest to absorb power.
I hope this helps.
Cheers,
Rod.