For complex systems that experience Multiple Dependent Competing Failure Processes (MDCFP), the dependency among the failure processes presents challenging issues in reliability modeling. This article, develops reliability models and preventive maintenance policies for systems subject to MDCFP. Specifically, two dependent/correlated failure processes are considered: soft failures caused jointly by continuous smooth degradation and additional abrupt degradation damage due to a shock process and catastrophic failures caused by an abrupt and sudden stress from the same shock process. A general reliability model is developed based on degradation and random shock modeling (i.e., extreme and cumulative shock models), which is then extended to a specific model for a linear degradation path and normally distributed shock load sizes and damage sizes. A preventive maintenance policy using periodic inspection is also developed by minimizing the average long-run maintenance cost rate. The developed reliability and maintenance models are demonstrated for a micro-electro-mechanical systems application example. These models can also be applied directly or customized for other complex systems that experience multiple dependent competing failure processes.