We propose exact hybrid methods based on integer linear programming and constraint programming for an integrated employee timetabling and job-shop scheduling problem. Each method we investigate uses a constraint programming (CP) formulation associated with a linear programming (LP) relaxation. Under a CP framework, the LP-relaxation is integrated into a global constraint using in addition reduced cost-based filtering techniques. We propose two CP formulations of the problem yielding two different LP relaxations. The first formulation is based on a direct representation of the problem. The second formulation is based on a decomposition in intervals of the intervals of the possible operation starting times. We show the theoretical interest of the decomposition-based representation compared to the direct representation through the analysis of dominant schedules. Computational experiments on a set of randomly generated instances confirms the superiority of the decomposition-based representation. In both cases, the hybrid methods outperforms pure constraint programming for employee cost minimization while it is not the case for makespan minimization. The experiments also investigate the interest of the proposed integrated method compared to a sequential approach and show its potential for multiobjective optimization