So the father knew (egnō oun ho patēr). Second aorist active indicative of ginōskō. Inferential use of oun.
Himself believed (episteusen autos). Not just the word of Jesus (Joh 4:50), but complete faith in Jesus himself as the Messiah, absolute use of pisteuō as in Joh 1:7.
And his whole house (kai hē oikia autou). All his family, the first example of a whole family believing in Jesus like the later case of Crispus (Act 18:8).