You can expect to make more of investing, over the long term, as long as the returns you expect from investing (7%) are greater than the interest rate on your mortgage (around 2.75% these days). Over the short term, it's anyone's guess. We focused on paying down our mortgage early on and now I wish we had invested that money. We still have a mortgage (albeit a smaller one) but that money would have served us better invested over the last 6 years.
Further to my point about above about convincing your wife (and one of the things I wish I understood better early on), is the importance of TIME in investing. I'm sure you've seen examples like this before, but say you start investing $1500 a month when you are 20, by the time you are 50, assuming 7% returns, you should have 1.8 million in investments, while having contributed 540,000. If you start at 35 and you invest 3000 per month (double the monthly amount), by the time you are 50 you will have about one million and you will have contributed the same 540,000. That's a huge difference between 1.8 million and 1 million! And if your money was kept in things that "won't lose money", you would have less than the 540,000 you saved because of inflation.