The method that Critter-3 suggested will not let you use your capital losses to offset the gain from the sale in the joint account. Here's another way to do it, which might actually be simpler than calculating the tax effect of the sale and "settling up" informally.
The family member does have to report the full amount of the sale on their tax return. But they received the 1099-B as a nominee for you. They can report the sale with a nominee adjustment (on Form 8949) for your share of the gain. The adjustment will remove your share of the gain from their tax return. You then report your share of the sale on your tax return as an investment sale for which you did not receive a 1099-B. That will put your share of the capital gain on your tax return, where it can be partially offset by your capital losses.
If it happens that your tax rate on capital gains is not the same as your family member's rate, the nominee procedure will also insure that your share of the gain is taxed at your rate.
