Networked microgrid (NMG) system is an effective solution to enhance the power system's reliability and resilience. The distributed control is promising for NMG system due to its high reliability, scalability and low computational burden. The distributed control relies on the information exchange among distributed generators and sub-microgrids (sub-MGs), which inevitably contain heterogenous time delays that can deteriorate system stability. This paper focuses on the multiple time-delays small-signal stability analysis of a DC NMG with a distributed layered control architecture. Firstly, a generalized time-delayed DC NMG small-signal model with a typical two-layer distributed control framework is developed. Then, stability analysis is conducted considering multiple time delays from communication and measurement stages in NMG layer and MG layer. The impact of multiple time delays on NMG stability is quantified. We reveal that both the electrical coupling among MGs and different kinds of time delays in distributed control loops will impact the NMG stability. Subsequently, based on the detailed analytical results, the critical eigenvalue is identified, and a new lead-lag compensation controller is proposed to enhance the system stability by compensating for the phase lag of the critical eigenvalue. Lastly, the effectiveness of the proposed method and the accuracy of the analytical findings are verified by OPAL-RT-based real-time tests.