This resourcepack has custom models but textures are not included because the models uses the default ones. I'm sorry for this problem, if you want i can update the pack trying to fix this.

Change the order of this pack and the one you are using in this screenshot? It's using the wrong texture on the right model, so if this pack is above your other one and it still has this issue (it will) you have to add the two lantern textures from default into this pack to force it. They are located in the minecraft .jar file for whatever version you are using. Just place the lantern.png and soul_lantern.png textures into the "textures" folder of this pack.

Thank you!