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We consider a $d$-dimensional branching particle system in a randomenvironment. Suppose that the initial measures converge weakly to a measurewith bounded density. Under the Mytnik-Sturm branching mechanism, we prove thatthe corresponding empirical measure $X_t^n$ converges weakly in the Skorohodspace $D([0,T];M_F(\mathbb{R}^d))$ and the limit has a density $u_t(x)$, where$M_F(\mathbb{R}^d)$ is the space of finite measures on $\mathbb{R}^d$. We alsoderive a stochastic partial differential equation $u_t(x)$ satisfies. By usingthe techniques of Malliavin calculus, we prove that $u_t(x)$ is jointlyH\"{o}lder continuous in time with exponent $\frac{1}{2}-\epsilon$ and in spacewith exponent $1-\epsilon$ for any $\epsilon>0$.

H\"{o}lder continuity of the solutions to a class of SPDEs arising from multidimensional superprocesses in random environment