Your husband is right about the Panasonic GH4 being better than the Canon T5i but almost 3 times the cost
Facts:
Advantages of the Panasonic DMC-GH4
Higher resolution movies 3840 x 2160 @ 30fps vs 1080p @ 30fps>>> Shoots higher resolution standard resolution video
Weather sealed Yes vs No >>>> Sealed to shoot in the rain
Better image quality 74.0 vs 61.0 >>>>More than 20% better image quality
More focus points 49 vs 9 >>>Set focus accurately within the frame
Phone cameras can not compare to a DSLR or mirror-less camera like the sony a6000