This is a great question!
The IRS is not 100% clear on this. IRS publications do however very strongly suggest that assuming your wife has a plan providing family coverage, you can contribute up to your family maximum.
If she does NOT have a family coverage plan then the answer is definitively no, you may only contribute the individual limit. Note if you have children covered by her plan then she is considered to have "family coverage" even if you are not covered by her plan (see here, question 12).
Latest IRS HSA Publication
From the 2012 IRS publication, bottom of Page 4.
For 2012, if you have self-only HDHP coverage, you can contribute up to $3,100. If you have family HDHP coverage, you can contribute up to $6,250.
This is presumably the referencing the definition which is introduced and discussed for married couples on Page 6:
Rules for married people.
If either spouse has family HDHP coverage, both spouses are treated as having family HDHP coverage. If each spouse has family coverage under a separate plan, the contribution limit for 2012 is $6,250. You must reduce the limit on contributions, before taking into account any additional contributions, by the amount contributed to both spouse's Archer MSAs. After that reduction, the contribution limit is split equally between the spouses unless you agree on a different division.
Example. For 2012, Mr. Auburn and his wife are both eligible individuals. They each have family coverage under separate HDHPs. Mr. Auburn is 58 years old and Mrs. Auburn is 53. Mr. and Mrs. Auburn can split the family contribution limit ($6,250) equally or they can agree on a different division. If they split it equally, Mr. Auburn can contribute $4,125 to an HSA (one-half the maximum contribution for family coverage ($3,125) + $1,000 additional contribution) and Mrs. Auburn can contribute $3,125 to an HSA.
The last example is nearly the exact situation you are in assuming your wife's plan is family coverage. The only assumption beyond what is explicitly written you need to make is that you are considered to have family coverage in the example as per the "Rules for married people" section, even though your plan only is a single-coverage plan.
This conclusion seems to logically follow from information in the FAQs here (see Q32), as well as this document.
Neither the above example nor any IRS documents referenced in this answer cover your situation completely.