As mobile networks progress towards a unified framework for integrated sensing and communication (ISAC), it is foreseeable to introduce new privacy concerns, particularly the potential exposure of position information to unintended receivers. In other words, the scope of physical-layer security (PLS) needs to be expanded to encompass both communication and sensing privacy. Therefore, in contrast to conventional PLS schemes that focus predominantly on preventing eavesdropping, this paper proposes a novel physical-layer privacy (PLP) design within ISAC frameworks, in order to guarantee the secrecy of data transmission while obscuring transmitter’s directional information. Specifically, we introduce a metric termed angular-domain peak-to-average ratio (ADPAR) to assess sensing resistance (SR) performance. Subsequently, three fundamental optimization problems are formulated under such ADPAR constraints to enhance communication secrecy, depending upon the integrity of illegitimate channel state information. These problems are then tackled using advanced strategies such as null-space projection and the cooperation with artificial noise. Additionally, closed-form solutions are further derived in a few specific cases by leveraging singular value decomposition (SVD) and generalized SVD. Finally, simulation results affirm the effectiveness of our design in safeguarding the twofold privacy within ISAC networks.