Is it permissible for a wife to read the Qur'an with her husband while he is ahead of her in completing the recitation (khatmah), on the condition that she will make up what she missed later, or is arrangement (tartib) necessary for completing the recitation?

There is no harm in reading with your husband and then making up for what was missed, because it is not a condition for completing the Quran that it be recited in sequence. In Mecca, they used to assign a man to record the letters and other parts the Imam omitted so that they could be recited on the night of the Khatmah (completion), thereby perfecting the Khatmah and fulfilling the reward.