If you husband is entering as part of the visa waiver program and you are an American citizen, then, no, he does not need to leave the country when you file. You should also file the I-485 along with the I-130 becuase, since he is married to an American citizen and had a legal entry, he is eligible to adjust status inside of the United States.
Your husband can adjust status within the US by filing forms I-130 and I-485.
Adjustment of status requires legal entry, inspection by an immigration officer at the port of entry.
He can also apply for travel document while his adjustment is pending should he wish to travel, assuming he does not overstay the 3month period prior to application.
If you are not familiar with the immigration process it is always advisable to contact an immigration lawyer to assist you in this process.
You are welcome to contact me via the link provided below if you wish to discuss your case.