He was a student of Yochanan Ben Zakkai. According to Bava Batra 134a, Yochanan Ben Zakkai was a Talmid of Beth Hillel but also a Talmid of Beth Shammai. This is why I wonder which House follow Rabbi Yehoshoua ben Hanania.
Also, Rabbi Eliezer was a talmid of Yochanan Ben Zakkai but followed beth Shammai (Yerushalmi Nazir 6:11). This is another reason why I wonder about the affiliation of Rabbi Yehoshoua.