Does "Seorang suami adalah pasangannya istri" also make sense?

It makes sense in the sense that it's a correct and perfect literal translation of the English sentence.
"a husband" = "seorang suami"
"the spouse of" = "pasangannya"

You can also use the classifier/counter "seorang" like this :
"Seorang suami adalah pasangan seorang istri."
"Seorang suami adalah pasangannya istri"

Both translations are correct.
However, you can omit the classifier, especially in a sentence like this where you're making a general statement.
It's much easier, much more straightforward to simply say :
"Suami adalah pasangan istri."