The jar of manna was placed, “In front of the covenant” in Exodus 16.
***Moses said, “This is what the LORD has commanded. Keep a full omer of it for your future generations, so that they may see the food I gave you to eat in the wilderness when I brought you out of the land of Egypt." Moses then told Aaron, “Take a jar and put a full omer of manna in it. Then place it before the LORD *to keep it for your future generations.” As the LORD had commanded Moses, Aaron placed it in front of the covenant to keep it. (Exodus 16:32-34)
Aaron’s staff was placed, “I front of the covenant” in Numbers 17.
Then the LORD said to Moses: Put back Aaron’s staff in front of the covenant, for safe keeping as a sign to the rebellious, so that their grumbling against me may cease and they might not die. Moses did this. Just as the LORD had commanded him, so he did. (Numbers 17:25-26)
“In front of the covenant” is taken to have meant inside of the ark, next to the two tablets on which the ten commandments were written.
The reference to the rod and manna in Hebrews is pretty clear, but my very brief search did not turn up any references in the Talmud or Mishna or other Jewish writings about what could have been in the ark.
-Tim-