For Banach algebras $\mathcal{A}$ and $\mathcal{B}$, we show that if $\mathcal{U}=\mathcal{A}×\mathcal{B}$ is commutative (weakly commutative), then each bi-Jordan homomorphism from $\mathcal{U}$ into a semisimple commutative Banach algebra $\mathcal{D}$ is a bi-homomorphism. We also prove the same result for 3-bi-Jordan homomorphism with the additional hypothesis that the Banach algebra $\mathcal{U}$ is unital.