Yes it is possible to reschedule the interview. If the interview is for your wife's immigration matter she should have an approved advance parole before she leaves. If the interview is for you then disregard the advance parole unless you are going too. There will not be any set time for the new interview. You should let the immigration officer now as soon as possible about the delay.
The answer provided here is general in nature and does not take into account other factors that may need to be reviewed for a more precise answer. You should consult with an immigration attorney before taking any action. The answer here is not intended to create an attorney-client relationship.
Yes, rescheduling the interview should not be a problem. She needs to contact immigration and make her situation known before she leaves and, as Mr. Murphy indicated, request advanced parole. I'd recommend you gather appropriate documentation to support the urgency of the situation, just in case her sudden departure causes problems when she goes through the interview. You won't be able to select your next date; Immigration will assign it to you.
You can make this request ... but you had better give detailed reasons for the emergency and why it can't be delayed by a few weeks.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
The reschedule request must be in writing. It is likely granted. However, the interview date may be pushed much much later.
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You are permitted to request to reschedule the interview, however there is no guarantee as to when the interview will be rescheduled to. You must appear at USCIS Infopass in person and request the change in writing.