Muslims are commanded by the Noble Qur’an (33:56) to send their prayers upon the Prophet Muhammad in which Allah has said:
‘Indeed God and His angels bless the Prophet; O you who have faith! Invoke blessings on him and invoke Peace upon him in a worthy manner.’
The Prophet indicated how to do this and also commanded his followers not to send their prayers only upon himself, but always to send their prayers simultaneously upon his family as well. He is quoted to have said:
‘Do not send me an amputated prayer.’ The companions asked, ‘What is an amputated prayer?’ He said, ‘When you say, ‘Allahumma, salli ‘ala Muhammad’ and stop. Rather, you should say, ‘Allahumma, salli ‘ala Muhammad wa al-e-Muhammad.’
The supplication will be intercepted (not accepted) until it is prayed upon the Prophet and his family.
On the authority of ‘Abdullah ibn Abi Layla, as reported by Imam al-Bukhari, the Messenger of Allah came to us and we said to him, ‘We have learned how to invoke peace upon you; how should we pray for you?’ He (the Prophet) said, ‘Say: O Allah, bless Muhammad and his family as You blessed the family of Ibrahim. Verily, You are the Praiseworthy, the Glorious. Grant favor to Muhammad and the members of his household as You granted favor to the members of the household of Ibrahim in the world. Verily, You are the Praiseworthy, the Glorious.’
When teaching his companions the salat (prayer), the Prophet specifically included his progeny (al-e-Muhammad). Hence, Muslims must adhere to the teachings of the Prophet and send blessings upon all of those whom he commanded for us to do.
 Yanabi’ al-Muwaddah, Vol. 2, 59; Ibn Hajar, al-Sawa’iq al-Muhriqah, Ch. 11. Sect. 1
 Yanabi’ al-Muwaddah, Vol. 2, 59
 Sahih al-Bukhari, “Book on Traditions of Prophets” Hadith 3119, “Interpretation of the Noble Qur’an” Hadith 4423, “Supplication” Hadith 5880; Sahih Muslim, “Book on Prayer” Hadith 614; al-Tirmidhi, “Book on Prayer” Hadith 445; al-Nisa’i, “Book on Inattention” Hadith 1270-1272; Abu Dawud, “Book on Prayer” Hadith 830; Ibn Majah, “Book on Immediate Call for Prayer” Hadith 894; Musnad Ahmad ibn Hanbal, Vol. 4, 241, 243, and 244; al-Darami, “Book on Prayer” Hadith 1308