Novel AFX/CHA aluminosilicate intergrowth zeolites ZTS-1 and ZTS-2 were synthesized using the dual structure-directing agent (dual-SDA) approach. ZTS-1 was obtained using the 1,1′-(1,4-butanediyl)bis(1-azonia-4-azabicyclo[2,2,2]octane) dication (Dab-42+) and the N,N,N-trimethyl-1-adamantylammonium cation (TMAda+) as organic structure-directing agents (OSDAs) for AFX and CHA phases, respectively. The obtained materials were characterized by powder X-ray diffraction (XRD), scanning electron microscopy (SEM), inductively coupled plasma atomic emission spectroscopy (ICP-AES), electron diffraction, high-resolution transmission electron microscopy (HRTEM), solid-state 13C dipolar decoupled magic-angle-spinning nuclear magnetic resonance (13C DD/MAS NMR), thermogravimetric and differential thermal analysis (TG/DTA), CHN analysis, and N2 adsorption. The combined results of these characterizations and those of the DIFFaX simulation showed that the AFX/CHA ratio of ZTS-1 was 80–85% AFX and 15–20% CHA (based on the number of unit cells). Control of the AFX/CHA ratio by simple variation of the hydrothermal synthetic parameters proved to be challenging. The catalytic performance of Cu-loaded ZTS-1 was tested in the selective catalytic reduction of NOx with NH3 (NH3-SCR), and its higher hydrothermal stability compared to the Cu-loaded AFX catalyst was confirmed. ZTS-2 was synthesized using K+ instead of TMAda+, under synthetic conditions completely different from those used for ZTS-1. The AFX/CHA ratio of ZTS-2 was estimated as 15–20% AFX and 80–85% CHA, strongly indicating the possibility of controlling the above ratio.