"My wife finishes eating the bread."

Translation: Mia edzino finas manĝi la panon.

[Grimmslaw]

So am I correct in saying that, in Esperanto, gerunds are treated as infinitives?

[arbaro]

Not always. You can also change a verb to a noun by replacing -i with -ado (kuirado gravas = cooking is important). But whenever you have a multi-verb construction like "finishes eating", you're usually going to use the infinite for the second verb.

[balou67]

If you say "My wife finishes to eat the bread" you see the infinitive too :)