。
We will take your silence as consent.
Literal
Be-silent-is [nominalizer-の] [topic-は] consented [thing-もの] [quotative-と] interpret.
Two things to notice. The の after 黙っている turns 'being silent' into a noun phrase that can act as the topic. ~ものと解釈する is a stock formal phrase — 'interpret as such-and-such a thing' — using もの as a generic 'thing' marker before the quotative と. Common in legal, business, and bureaucratic Japanese.