Multi-slice　imaging　can　obtain　the　Three-dimensional(3D)　information　of　thick　objects　by　modeling　specimen　as　a　number　of　slices.　This　approach　can　be　applied　to　biomedical　imaging,　integrated　circuit　inspection　and　sample　thickness　measurement.　Multi-slice　ptychography　is　a　full-field　and　lensless　imaging　method　exploiting　3D　Ptychographic　Iterative　Engine　(3PIE)　algorithm　to　reconstruct　the　complex-value　function　of　object　planes　and　illumination　beams　simultaneously.　Even　though　this　method　does　not　require　prior　knowledge,　inaccurate　initial　guesses　of　the　object　planes　lead　to　more　iterations　than　for　a　single-slice　object.　Compressive　holography　(CH)　is　another　method　for　reconstructing　multi-slice　objects.　It　enables　to　obtain　3D　information　from　a　single　2D　Gabor　hologram　by　compressive　sensing　(CS)　algorithm.　In　this　paper,　both　methods　are　combined　and　the　corresponding　algorithm　is　proposed,　in　which　the　reconstructed　multi-slice　object　by　CH　is　adopted　as　the　initial　guess　for　object　planes　in　3PIE　providing　a　more　accurate　initial　value.　Experimentally,　the　ptychography　data　set　and　a　single　in-line　hologram　are　recorded　in　sequence.　The　numerical　simulation　studies　on　double-slice　and　three-slice　objects　were　conducted,　respectively.　Numerical　simulation　results　indicate　that　our　method　has　a　smaller　error　compared　to　traditional　methods　and　it　can　improve　the　convergence　speed.　The　proposed　method　was　experimentally　demonstrated　using　a　double-slice　object.　The　conclusions　drawn　from　the　experiments　are　in　agreement　with　the　simulations.　We　expect　our　method　to　provide　invaluable　information　for　both　the　life　and　materials　sciences.　©　2024　SPIE.