Direct numerical simulations are performed to investigate the mixing and dispersion of passive plumes emitted from two parallel line sources into a homogeneous isotropic turbulent flow. The focus of this study is on the turbulent convective regime of plume mixing, where the bulk meandering of the instantaneous plumes makes the primary contribution to the plume dispersion and concentration fluctuations. The quality of mixing and the interference between the two plumes have been studied in both physical and spectral spaces. It is found that the exceedance probability of high concentrations for the total plume released from dual sources is much smaller than that released from a single line source. The reduction in the exceedance probability across high concentration levels for the total plume is quantified using a reduction factor, whose value approaches unity as the cross correlation coefficient between the two concentration fields becomes increasingly positive. It is observed that the scatterplots of the normalized third- and fourth-order concentration moments against the normalized second-order concentration moment collapse onto a single curve, indicating that higher order concentration moments of the total plume can be determined effectively from the information on lower order concentration moments. Furthermore, it is demonstrated that the concentration probability density function for the total plume can be properly evaluated using a clipped-gamma model. In the spectral analysis, the results of the pre-multiplied co-spectra and coherency spectra reveal that the mixing process is the strongest and fastest at large scales for the turbulent convective regime of plume mixing.