Dissipative Kerr solitons are localized structures that exist in nonlinear optical cavities. They lead to the formation of microcombs¿chip-scale frequency combs that could facilitate precision frequency synthesis and metrology by capitalizing on advances in silicon photonics. Previous demonstrations have mainly focused on anomalous dispersion cavities. Notwithstanding, localized structures also exist in the normal dispersion regime in the form of circulating dark pulses, but their physical dynamics is far from being understood. Here, we explore dark-pulse Kerr combs generated in normal dispersion optical microresonators and report the discovery of reversible switching between coherent dark-pulse combs, whereby distinct states can be accessed deterministically. Furthermore, we reveal that the formation of dark-pulse Kerr combs is associated with the appearance of another resonance, a feature that has never been observed for dark pulses and is ascribed to soliton behavior. These results contribute to understanding the nonlinear physics in normal dispersion nonlinear cavities and provide insight into the generation of microcombs with high conversion efficiency.