Should he have intercourse with his menstruating wife and pay the expiation because her menstrual cycle is so long?
Question

                My period lasts ten days, and then I find yellowish discharge for another five days. This offends my husband a lot as he cannot tolerate this. Is he allowed to have an intercourse with me before then ten day ends then pay expiation? Especially that I have only 16 days between the two periods.
Praise be to Allah.
    Firstly: 

    If the yellowish discharge comes straight after the menses 
    then it is part of the menses, and it is not permissible at that time to 
    have intercourse or to pray or fast. If the yellowish discharge comes after 
    the end of the menses (tuhr), then it is not counted as anything. 

    As for the yellowish discharge that comes directly before the 
    menses, if it is accompanied by the pains of menses (cramps) that happen to 
    women, then it is menses; if it is not accompanied by pains, then it is not 
    menses. 

    See the answer to question no. 
    37840. 

    The end of menses (tuhr) occurs when one of two signs appear: 
    the emission of a white discharge, or when the place becomes dry, so that if 
    a piece of cotton etc is inserted it comes out clean with no trace of blood 
    or yellowish or brownish discharge. 

    Secondly: 

    It is not permissible for the husband to have intercourse 
    with his wife during her menses, because Allaah says (interpretation of the 
    meaning): 

    “They ask you concerning menstruation. Say: that is an 
    Adha (a harmful thing for a husband to have a sexual intercourse with his 
    wife while she is having her menses), therefore, keep away from women during 
    menses and go not unto them till they are purified (from menses and have 
    taken a bath). And when they have purified themselves, then go in unto them 
    as Allaah has ordained for you (go in unto them in any manner as long as it 
    is in their vagina). Truly, Allaah loves those who turn unto Him in 
    repentance and loves those who purify themselves (by taking a bath and 
    cleaning and washing thoroughly their private parts and bodies for their 
    prayers)”

    [al-Baqarah 2:222]. 

    So it is not permissible to have intercourse with a 
    menstruating woman until she becomes pure (her menses ends) and she has done 
    ghusl.

     There is a stern warning against having intercourse with a 
    menstruating woman, as was narrated by al-Tirmidhi (135), Abu Dawood (3904) 
    and Ibn Majaah (639) from Abu Hurayrah (may Allaah be pleased with him) from 
    the Prophet  (peace and blessings of Allaah be upon him) who said: 
    “Whoever has intercourse with a menstruating woman, or with a woman in her 
    back passage, or who goes to a fortuneteller and believes what he says, has 
    disbelieved in that which was revealed to Muhammad.” Classed as saheeh by 
    al-Albaani in Saheeh al-Tirmidhi. 

    The husband may enjoy his menstruating wife in ways other 
    than intercourse. See question no. 
    36722. 

    The wife does not have the right to agree to this evil, 
    rather she must refuse. 

    The husband must fear Allaah and beware of haraam forms of 
    intimacy. In that which is halaal there is sufficient. In addition to being 
    haraam, having intercourse during menses is harmful to both the man and the 
    woman. See question no. 43028. 

    And Allaah knows best.