Density is known to be difficult to reconstruct in multiparameter full-waveform inversion (FWI). This difficulty results from the similarity of the diffraction patterns of velocity and density at small scattering angles. In addition, the sensitivities of seismic data with respect to velocity and density have different orders of magnitude which make the inversion ill-conditioned. The inverse Hessian has been shown to mitigate the coupling effects and rescale the magnitudes of different parameters, such that reliable updates for all parameters are available. We have investigated the possibility of simultaneous estimations of velocity and density in acoustic media using the truncated Gauss-Newton method. The model updates are calculated using a matrix-free conjugate gradient solution of the Gauss-Newton normal equation. The gradients of the misfit function with respect to the model parameters and the Hessian-vector products are computed using an improved scattering-integral approach. To give some insights into the trade-off effects between velocity and density, and the imaging resolution in FWI, the sensitivity kernels of both parameters are numerically calculated in homogeneous background models, and their spatial distributions and characteristics are analyzed. The synthetic experiments on a canonical inclusion model and the 2004 BP model confirm that, in cases in which the Gauss-Newton approximate Hessian, especially its off-diagonal blocks, is accurately taken into account, the truncated Gauss-Newton method can effectively mitigate the trade-off effects between velocity and density and provide accelerated convergence rate. Hence, well-resolved velocity and density models are expected.