This paper presents the first ever approach for solving continuous-observation Decentralized Partially Observable Markov Decision Processes (Dec-POMDPs) and their semi-Markovian counterparts, Dec-POSMDPs. This contribution is especially important in robotics, where a vast number of sensors provide continuous observation data. A continuous-observation policy representation is introduced using Stochastic Kernel-based Finite State Automata (SK-FSAs). An SK-FSA search algorithm titled Entropy-based Policy Search using Continuous Kernel Observations (EPSCKO) is introduced and applied to the first ever continuous-observation Dec-POMDP/Dec-POSMDP domain, where it significantly outperforms state-of-the-art discrete approaches. This methodology is equally applicable to Dec-POMDPs and Dec-POSMDPs, though the empirical analysis presented focuses on Dec-POSMDPs due to their higher scalability. To improve convergence, an entropy injection policy search acceleration approach for both continuous and discrete observation cases is also developed and shown to improve convergence rates without degrading policy quality.