We study a mixed singular control/optimal stopping problem for an insurance company. The manager has the possibility of switching among several regimes; in each of the regimes, the uncontrolled surplus of the company evolves as a different compound Poisson process with drift. Switching among regimes could produce an instantaneous transition cost or benefit. The manager pays dividends to the shareholders, and the goal is to find the dividend payment policy and the switches among regimes (times and destinations) which maximize the expected cumulative discounted dividend pay-outs until the ruin time. We address both the cases of irreversible and reversible switching. These problems can be seen as obstacle problems. We characterize the optimal value function as the smallest viscosity solution of the associated Hamilton-Jacobi-Bellman equation. We prove that there exists an optimal dividend and switching strategy and that this strategy is stationary with a band structure. We find a verification result to check optimality even in the case where the optimal value function is not differentiable. We present numerical examples of irreversible switching (optimal time for acquisition of another company and optimal time for disinvestment of a branch of the company) as well as an example of reversible switching. In some of these examples, the value function is neither concave nor differentiable.