Since he took the third daughter of Tadataka HOSOKAWA (after the disinheritance, he called himself NAGAOKA Kyumu), Fukuhime (Princess Fuku) (1609-1635) as his lawful wife, and as Tadataka was the first son of the lord of Higo domain, Tadaoki HOSOKAWA, even after Fukuhime's death, he continued to be granted the yield of rice from the Hosokawa clan.
通式が肥後藩主細川忠興の長男細川忠隆（廃嫡後は長岡休無）の三女福姫（1609-1635）を正室にした由縁で、福姫死後も助成米が細川氏から送られている。