Drupal 7 Views filter between two dates
First of all if you have date module you do not need to add two fields "Post" and "Expire". You can add a date field with a start and an end date. Other than that the rest is simple. Go to your view and add two filters.

First filter will be your start date where the field is "less than or equal to" -> "now" (you can write that only if you select "enter a relative date" )

Second filter as you may have guessed will be your expire date field where the field is "is greater than or equal to" -> "now"

If "less than or equal to" and "greater than or equal to" don't appear as options, make sure you've enabled the Date Views module. (It is installed as part of the Date project.)