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