飲み歩く is a compound verb 飲む + 歩く ('drink + walk around'), meaning 'to pub-crawl, to drink all over town.' ~てばかりいる ('do nothing but X,' 'always X-ing') expresses habitual, excessive engagement. 愛想を尽かす is the set idiom 'to be fed up with,' 'to lose all patience with' — and the passive 尽かされる makes the husband the target of the wife's exhaustion. The final ぞ is a stern masculine warning. A colorful, scolding sentence.