。
My husband and daughter are fast asleep.
Literal
Husband [and-と] daughter [topic-は] soundly [adverbial-と] are-sleeping.
ぐっすり is a 擬態語 (state mimetic) specifically for deep, untroubled sleep — Japanese has a family of sleep mimetics distinguishing qualities (うとうと for dozing, こっくり for nodding off) where English uses adjectives. The optional と after it is the adverbial particle characteristic of mimetics, distinct from the conjunctive と joining 夫 and 娘 in the same sentence. ~ている on 眠る marks the resulting state of being asleep — 眠る as a change-of-state verb means 'to fall asleep,' so 眠っている is 'is in the state of having fallen asleep,' i.e., 'is sleeping.'