Different TSH assays can have greater/lesser sensitivity. (Meaning supersensitive TSH tests often come back fairly high relative to the true degree of disease.)
Was a free T4 done? (This is a measure of the actual thyroid hormone.) A TSH of 7 is only mildly elevated (assuming the units are the same as what I am familiar with). If the TSH is mildly elevated and the free T4 is normal, this would actually represent subclinical hypothyroidism. Subclinical hypothyroidism is not necessarily the same as hypothyroidism (generally implies a higher risk of developing hypothyroidism in the future, but not everyone would agree that this needs to be treated with thyroid medication- many people would just watch this over time).
I haven't seen your test results and I don't want to butt in too much, but your DH might be right. It may be worth asking to have the test repeated, or making an appointment to see the doctor to make sure you have the full information.