Each application is considered independently of the other. As it typically takes between 3 and 8 months for the naturalization interview to be scheduled after filing, depending on the jurisdiction, but is the about the same amount of time in any particular jurisdiction, there is a possibility that you could be interviewed on the same day purely by chance. However, I would say that more probably not not you would not be interviewed on the same day. Approximate processing times for N400 applications are available on the USCIS website.
Hard to tell if you will be interviewed together. It takes 3-6 months to get an interview.
Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
It is not unusual for your applications to be reviewed and set for interviews at different times. The interview after the yellow letter could take any time, but usually between 4-9 months. There is no certain date for the interview time. USCIS sets its own schedule. It is very doubtful that you will be interviewed on the same day. I hope these answers helped you understand the process.
You may contact the Law Office of Robin J. Gray for further legal advice. Office (610) 689-0877; Fax (610) 689-0932; Cell (484) 769-5855; robingraylaw.com This answer is for informational purposes only. It does not establish an attorney client relationship.
Since your wife is already scheduled for interview and you are not, I would say that there is zero chance that you will be interviewed on the same day. Even though you may have filed your applications on the same day, they are two separate files and they are not kept together. So it is not unusual for the interviews to be on different dates. There is no typical period after the yellow letter comes until you are scheduled for interview. It could be two weeks or it could be longer.