A wireless network operator typically divides the radio spectrum it possesses into a number of subbands. In a cellular network those subbands are then reused in many cells. To mitigate co-channel interference, a joint spectrum and power allocation problem is often formulated to maximize a sum-rate objective. The best known algorithms for solving such problems generally require instantaneous global channel state information and a centralized optimizer. In fact those algorithms have not been implemented in practice in large networks with time-varying subbands. Deep reinforcement learning algorithms are promising tools for solving complex resource management problems. A major challenge here is that spectrum allocation involves discrete subband selection, whereas power allocation involves continuous variables. In this paper, a learning framework is proposed to optimize both discrete and continuous decision variables. Specifically, two separate deep reinforcement learning algorithms are designed to be executed and trained simultaneously to maximize a joint objective. Simulation results show that the proposed scheme outperforms both the state-of-the-art fractional programming algorithm and a previous solution based on deep reinforcement learning.