The optical properties of light absorbing soot aerosols generally change through interactions with weakly absorbing particles, resulting in complex mixing states, and have been highlighted as a major uncertainty in assessing their radiative forcing and climatic impact. The single scattering properties of soot aggregates partially embedded in the host sulfate particle (semi-embedded soot-containing mixtures) are investigated for two kinds of morphologies with intersecting and non-intersecting surfaces. The surfaces cannot be overlapped in the non-intersecting surface morphology, while the intersecting surface morphology is unconstrained. Based on the modified diffusion limited aggregation (DLA) algorithm, the models with non-intersecting surfaces are simulated and applied for the single scattering calculations of semi-embedded soot-containing mixtures using the superposition T-matrix (STM) method. For comparison, the models with intersecting surfaces are simulated with the same morphological parameters, but some soot monomers are intersected by the host sphere. Due to the limitation of current STM method, the optical properties of these models with intersecting surfaces are calculated using the discrete dipole approximation (DDA) method. The soot volume fractions outside sulfate host are introduced and applied to characterize the mixing states of the soot-containing aerosols. These simulations show that the absorption cross-sections of those internally, deeply, half and slightly embedded mixed soot particles are ~105%, ~65%, ~43% and ~14% larger than the semi-external mixtures , respectively. The results also indicate that the differences of extinction cross-sections, single scattering albedo (SSA) and asymmetry parameter (ASY) between simulations with intersecting and non-intersecting surfaces are small (<1%) for semi-embedded soot-containing mixtures with the same morphological parameters. Within the range of visible and near-infrared wavelengths, the relative deviations of absorption cross-sections between these different morphologies are also small (<~5%). Therefore, based on these simulations, the single scattering properties of semi-embedded soot-containing mixtures are rarely influenced by the morphological differences between the absorbing spheres intersecting and non-intersecting the non-absorbing host, which can nearly be ignored in the single scattering calculations.