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This paper deals with the design of an energy-to-peak reduced-order filter (also called $L_{2}-L_{\infty }$ filtering) for continuous-time Markov jump linear systems, assuming that the filter has only access to an estimate of the Markov parameter, coming from the output of a detector device. To model this situation we consider that the joint process formed by the Markov parameter and the detector information follows an exponential hidden Markov model. The result is given in terms of Linear Matrix Inequalities (LMI) so that the available numerical package tools can be readily implemented to solve the problem. The paper is concluded with some numerical simulations.