There are going to be a lot of people on here who are going to mention "buy term and invest the difference" because they've been fed information from Dave Ramsey and other financial entertainers that whole life or universal life is a bad "investment". But that's not your question and you're looking to have growth and liquidity, so an insurance vehicle can help you here.
An Indexed Universal Life policy is an asset that has underlying investments (index funds), but there's also an insurance expense which is basically term each year. Using it for what you've mentioned is an alternative source of financing that has tax advantages if done right, but the devil is in the details. That insurance expense will increase as you age, but if you keep enough cash in the policy then that will help to mitigate that increase in cost. If you don't keep it well funded there's a possibility in can lapse. The policy should be a non-recognition policy (they still pay interest and dividends based on your cash value amount and don't recognize any loans you have out on the policy when making these), and a mutual company would (most likely) be best since the dividends won't be taxed, and can still be reinvested into the policy.
As for the mutual funds - that's more along the lines of a variable product and there are more fees and risk than an indexed policy, plus it's difficult to consistently beat the index. You seem like you still want it to provide a life insurance benefit, so just use caution in deciding how much risk you want this to be exposed to (risk is related to control, not always reward).
Disclaimer - I am licensed to sell life insurance and we do this exact type of investing with clients, so it can be done if set up correctly, but it's not an "off-the-shelf" type of product. If properly designed and used, you can do very well with it. I would look for someone who works in your area that has done this successfully. I'm with MassMutual (we use a whole life product for this instead of an indexed universal policy), and there are some Guardian, and Northwestern Mutual policies among others that also work well for these.
Good luck in your search.