Well, your husband is right about the sharp of one note being the flat of the next higher note.  More or less.

Presuming "equal temperament" on the tuning/intonation, then they should be the same.  That is the most common modern convention, and if we assume that is being used, then your husband would be right.

However, there are other ways of figuring the "correct" notes in the octave, more used in older music like classical, romance, baroque and etc.  Some people feel they simply sound better than a simple bit of decimal/digital math.  This is why sometimes if you use your electronic tuner to watch the notes when a very good player of such music is playing on a video or other recording, you may notice that they will consistently be a bit "out of tune" on certain notes when playing in certain keys.  That gave every different key signature a slightly different sound.  The difference is subtle, but definitely there.

So composers at least used to write with that in mind, since a melody played in one key might sound a bit more sad while it would sound a bit more "triumphant" or joyful in another key.  Some modern composers still follow that idea of different keys having different colours or flavours to them.

You play guitar, and the guitar and similar fretted instruments are impossible to tune for a 100% equal temperament.  So on guitar, each key you play in actually does have a subtle difference in how a melody or chord pattern will sound.  It is also why different voicings played up the neck can have a slightly different feel to them than when they are voiced in chords down with the open strings.  You may notice it even more if you play against a piano or even more with most electronic keyboards which are usually very "equal tempered".  If you tune your open strings to the notes on those keyboards, and then check notes up the neck against that same keyboard, some of your notes on the guitar will sound very slightly "out of tune".  But your guitar still sounds in tune when you play play.  Because it *is* in tune, just by a slightly different logic.

Back in the era of instruments like harpsichords (for example), sometimes the C sharp and D flat (again, just for example, other notes might be similarly affected) would actually even have separate keys to be played, so an octave on those keyboards might have more than 12 keys! 

So there are some differences in some cases.  But in current modern music they will be much slighter than they would have sounded centuries ago.

With modern compositions, the key signature is usually picked because some keys are easier to play on some instruments, or the piece may be being written for or by someone who prefers to sing or play in a particular key. 

How is that for a whole lot more information than you wanted?  LOL  This is the sort of thing that scary people like musicologists might stay up nights arguing over. 

On one last point of trivia that might be slightly interesting to think about.. Bach's piece "The Well-Tempered Clavier" (most common English title for it) was intentionally written to be played on a keyboard that was tuned with something fairly close to the even temperament system in common use today, hence the title.  But many of his other pieces were not.  If you could put Bach into a time machine and bring him forward to hear some of his pieces (other than that one and a few others) being played on a modern electronic keyboard (or even most pianos these days), he might wonder why the modern instrument was "out of tune".