The simultaneous ordering of different degrees of freedom in complex materials undergoing spontaneous symmetry-breaking transitions often involves intricate couplings that have remained elusive in phenomena as wide ranging as stripe formation¹, unconventional superconductivity^{1, 2, 3, 4, 5, 6, 7} or colossal magnetoresistance^{1, 8}. Ultrafast optical, X-ray and electron pulses can elucidate the microscopic interplay between these orders by probing the electronic and lattice dynamics separately^{9, 10, 11, 12, 13, 14, 15, 16, 17}, but a simultaneous direct observation of multiple orders on the femtosecond scale has been challenging. Here we show that ultrabroadband terahertz pulses can simultaneously trace the ultrafast evolution of coexisting lattice and electronic orders. For the example of a charge density wave (CDW) in 1T-TiSe₂, we demonstrate that two components of the CDW order parameter—excitonic correlations and a periodic lattice distortion (PLD)—respond very differently to 12-fs optical excitation. Even when the excitonic order of the CDW is quenched, the PLD can persist in a coherently excited state. This observation proves that excitonic correlations are not the sole driving force of the CDW transition in 1T-TiSe₂, and exemplifies the sort of profound insight that disentangling strongly coupled components of order parameters in the time domain may provide for the understanding of a broad class of phase transitions.