So you are looking to change your current visa to a spousal visa so that you can stay in Japan, correct?
I just did this myself last month. You will need to take a number of documents to the immigration office to change your current visa to a spouse visa. Keep in mind if you haven't yet updated your place of residence so that it matches your husband then that would be the first thing to do (this caused me some trouble). Also, I am told that what you need to bring can vary depending on your employment situation as in the names of the documents may vary but essentially they contain the same info. The most definitive answer would be to call up immigration again and try to speak to someone who knows what they're talking about (which seems to be the main problem you're having).
Anyway, this is what I was told to bring (I am employed in Japan, my wife is Japanese and also employed). It should be fundamentally similar to what you'll need.
1. A copy of your husband's Koseki which lists you as his spouse.
2. If you are employed in Japan you need a Shotokushoumeisho which I believe shows how much you paid in taxes the previous year. If you are not employed you need to get one for your husband instead.
(items 1-2 are obtained at your city hall)
3. If you are currently employed you need to get a Zaishokushoumeisho from your employer which should include your start date at the company, your position and current salary, as well as the company inkan. If you are not employed than you need this from your husbands employer.
4. A letter of guarantee from your spouse. A template can be downloaded here:
http://www.educationjapan.org/forms/jfj002.pdf5. The Application for Change of Status of Residence form which can be found here along with an example of how to fill it out:
http://www.immi-moj.go.jp/english/tetuduki/kanri/shyorui/02....Bring those papers, your passport, and your alien registration card to your local immigration office. A list of the offices can be found here:
http://www.immi-moj.go.jp/english/info/index.htmlI highly recommend doing all the paperwork before getting there. You basically just turn it in and fill out your name and address on a postcard that they give you so that they can notify you by mail when to come back. They will contact you if there are any issues with your application or if they need you to submit more information.
When you receive the postcard back in the mail it will list a deadline to report to the immigration office. First go to the post office and pick up a Shuunyuu Inshi (revenue stamp) for 4000 yen which you bring with you and is the payment for the visa transfer. Report to the immigration office before the deadline with your inshi and postcard and get your new visa. If you plan on travelling you can get a reentry permit at the same time (don't forget to pick up an additional 3000 yen (single entry) or 6000 yen (multi entry) Inshi at the post office for the reentry permit fee)