The dynamics of diverse synchronization control, such as grid-following (GFL) and grid-forming (GFM) control, are complicating the oscillatory behaviors in multi-converter systems. In this context, the impedance network (IN) based frequency-domain modal analysis (FMA) method is useful for diagnosing oscillations. However, since the conventional impedance model retains only electric nodes, the FMA primarily reflects the circuit-related information, e.g., node participation factor, making it less intuitive for probing the synchronous dynamics. To address this issue, this paper proposes an augmented impedance network (AIN) modeling method by explicitly characterizing synchronous control loops for stability assessment. First, a four-port augmented impedance model (AIM) with an additional synchronization port is proposed for a generic AC/DC converter, and the corresponding AIN model of a generic AC/DC multi-converter system is formulated in a scalable approach. Then, the FMA method is generalized by simultaneously incorporating the electric nodes (including AC and DC nodes) and synchronous nodes. Finally, the AIN model and its associated FMA method are comprehensively validated in a typical point-to-point high-voltage direct current (HVDC) system and a modified IEEE 9-bus system, both with GFM and GFL converters.