Neural directional filtering (NDF) has been introduced as a flexible approach for reconstructing a virtual directional microphone (VDM) with a target directivity pattern for spatial sound capture. Building on this idea, we propose NDF+, which enables joint neural directional filtering and diffuse sound extraction. NDF+ reformulates VDM estimation into two coupled subtasks: dereverberated VDM reconstruction and diffuse sound extraction. This reformulation enables NDF+ to manipulate diffuse components in the final reconstructed VDM output. We evaluate NDF+ under reverberant conditions and compare it with representative conventional baselines. Results show that NDF+ consistently outperforms the baselines on both subtasks, while maintaining VDM reconstruction quality comparable to that of the original single-task NDF model. These findings indicate that NDF+ introduces an additional degree of freedom for diffuse sound control in the VDM reconstruction. In a stereo recording application, NDF+ provides controllable inter-channel level differences between left and right channels by adjusting the estimated diffuse component.