Splitting payments for large purchases among different methods of payments is not very obvious on Jared.com, but it is possible with this nifty trick.
The key to splitting payments is to put a portion of the overall payment for the item on a gift card. When the gift card is loaded with funds from one of your methods of payment, you can use it with a different form of payment easily.
The first step, of course, is to purchase a gift card from Jared.com. Be sure you don't select the option to have the gift card mailed to you, or else you may end up waiting for a while!
On the right you can see the various denominations that you can use for your gift card, or you can choose your own denomination.
On the left is what the card will look like when it arrives in your recipient address. The important elements here are the Gift Card # and the Pin #. Without those two bits of information you can't use the card to split a payment.
Next, begin check out on your purchase. When you start to check out, you'll see this page, but note that you will not use the "Promotional Code/Certificate" field for your gift card!
The page you get to when you click "Checkout" or "Sign In & Checkout" is where you will enter the Gift Card # and the Pin #.
Here, after you've entered your billing and shipping information, you'll be prompted to enter your credit card information. Above that is an option to apply a gift card. In the image, the option is expanded.
If you have any questions ask below in the comments and I'll try to answer them.