The word albeit historically also introduced an independent clause as although does (as in the Shakespearean quote above); however after the Early Modern English period, it ceased to do so, and today only introduces a noun phrase, adjectival phrase, adverbial phrase, or dependent clause.
Rarely, albethey is used when the meaning is “despite (the multiple things) being” rather than “despite (the single thing) being”; this is nonstandard, based on a flawed interpretation of albeit.