Exactly what she said. If he gets a B permit then you will get a B, if he gets an L then you will get an L. It depends on his contract unfortunately which may be too short to qualify him for a B permit. However, that shouldn't as far as I know cause a problem for you getting work.
It's outlined here: Are family members allowed to work in Switzerland?
Spouses and children of EU-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. Cantonal migration authorities Fact Sheet on Family Reunification https://www.bfm.admin.ch/bfm/en/home...-efta/faq.html
Since your husband is Dutch, the fact he may have an L permit shouldn't affect it. Note that initially your permit will only be for residence, but you just need to take your employment contract to the cantonal migration office to add the work part to it.