You need to put all the world files that tell you 'about the map' in the Data\world\maps\campaign\Hispania (in your case) folder. The only world files that the -mod:my_mod switch makes the game look for in your my_mod folder (CoH\world\maps\campaign\Hispania in your case) are those that are 'about the campaign'. Specifically:
descr_strat.txt
leader_pic_{faction}.tga
map_{faction}.tga

This should get your campaign working. Unfortunately, it seems that the -mod:my_mod switch is still not fully functional: you cannot play custom battles when using this switch.

If I copy all the files from my 'my_mod' folder into the data folder, and run the game without the switch, I can play custom battles no problem. But with the switch, it just stays at whatever screen it's at when you click the 'start battle' button, and gives no error on exit. The campaign works with the switch, as do battles within the campaign, but not custom battles. I've tried copying pretty much the entire contents (i.e. every sub-folder) of the data folder into the my_mod folder, but to no avail. Hence my arriving at the above conclusion: that custom battles do not work with the switch.

Has anyone managed to in fact get them to work using this switch?