Collaborative planning under operational constraints is an essential capability for heterogeneous robot teams tackling complex large-scale real-world tasks. Unmanned Aerial Vehicles (UAVs) offer rapid environmental coverage, but flight time is often limited by energy constraints, whereas Unmanned Ground Vehicles (UGVs) have greater energy capacity to support long-duration missions, but movement is constrained by traversable terrain. Individually, neither can complete tasks such as environmental monitoring. Effective UAV-UGV collaboration therefore requires energy-constrained multi-UAV task planning, traversability-constrained multi-UGV path planning, and crucially, synchronized concurrent co-planning to ensure timely in-mission recharging. To enable these capabilities, we propose Collaborative Planning with Concurrent Synchronization (CoPCS), a learning-based approach that integrates a heterogeneous graph transformer for operationally constrained task encoding with a transformer decoder for joint, synchronized co-planning that enables UAVs and UGVs to act concurrently in a coordinated manner. CoPCS is trained end-to-end under a unified imitation learning paradigm. We conducted extensive experiments to evaluate CoPCS in both robotic simulations and physical robot teams. Experimental results demonstrate that our method provides the novel multi-robot capability of synchronized concurrent co-planning and substantially improves team performance. More details of this work are available on the project website: https://hcrlab.gitlab.io/project/CoPCS.