The destruction of Israel will effect Judah. The same Assyria that will destroy Israel will bring waste and desolation to Judah.
Gileadi’s translation of this passage is clearer than the KJV:
The Lord will bring upon you and your people and your father’s house a day unlike any since Ephraim broke away from Judah - the day of the king of Assyria. (Gileadi, p. 109.)
The italicized “the day” is Gileadi’s insertion of text that he suggest is implied. The implication would come for the paralleling of the day “unlike any” and the coming of the king of Assyria. From the poetic parallels Isaiah incorporates into his writing, this reading continues the literary aspect of Isaiah better than simply reporting that the king of Assyria would come.
Isaiah is warning Ahaz that the alliance with the king of Assyria might bring some few years of peace (when a young man might be eating butter and honey, v. 15) but will eventually be a curse on Judah - a curse not seen since the internal strife surrounding the split of the Solominic kingdom.