Oops, sorry! I was thinking you were both non-EU. This is what you want:

"Are family members allowed to work in Switzerland?

Spouses and children of EU-27/EFTA nationals who are admitted to Switzerland under family reunification are legally entitled to work regardless of their nationality. However, they have to inform the appropriate cantonal migration authorities before doing so. Spouses and children of EU2 nationals who have a short-term (L) permit are subject to systematic controls by the cantonal migration authorities to ensure wage and working conditions are correspond to the particular region and sector."

https://www.sem.admin.ch/sem/en/home...hweiz/faq.html

Also a factsheet here which confirms:

https://www.sem.admin.ch/content/dam...nnachzug-e.pdf

To inform the authorities you just need to take your employment contract to the migration office which activates the work part of your residence permit, be it an L or B.