If supernatural includes belief in the unseen, such as angels, jinn, Paradise and Hell then yes we believe in this. We also believe that Mary was a virgin and that Allah said "Be!" and he was created by His Command. We also believe that sihr (sorcery/magic) and the 'Ayn (The Evil/Envious Eye) is a reality, as well as possession of humans by jinn. We believe that Allah's Messenger split the moon, as attested by his people, though, those who were against him claimed it to be magic. This is one of several examples of the miracles of Allah's Messenger, and we believe in all of them since mant of them are witnessed by his companions and enemies alike, and only those who believed in these signs that were by Allah's Will were guided.
Christians blindly follow their Book, which is known, with certainty, to have been altered by human hands. The Book is "perfect through faith", without any corroborating doctrine or text. In Islam, the Qur'an is corraborated by the Hadeeth (those who reject the authentic Hadeeth reject the Qur'an as well) as well as statements of the companions themselves and even the enemies of Islam during the time of the Revelation. Though, for the Western world, most of this is obscured by a discrepency in language, meaning, much of the Arabic has yet to be translated, although a sufficient amount can be found in English capturing the meaning.
Abdushakur, you have only presented your belief, but presented no evidences to these so-called "miracles" of your "Messenger".
The Qur'an also alluded to King Solomon being able to understand the languages of the ants (27:18-19) and birds (27:16, 20), and speak to it.
It also say that Solomon can control and command the winds, as well as command the jinns and birds to fight in his army (27:17).
Do you also believe in these passages?
Muhammad is spinning fables and fairytale about talking animals, having no basis in reality.
The Old Testament Bible also include talking serpent and talking donkey, but they are also just fables/myths. And just because the Qur'an also include talking birds and ants, it doesn't justify such "miracles" are true.
Fables, at least the written narratives, have existed for millennia, and the earliest known ones exist in religious texts written in Egyptian hieroglyphs and Sumerian cuneiform from the 3rd millennia BCE.
You said you believe in jinns and jinn in possessing people. What does say about jinns?
Jinn supposed to be a being made out of smokeless fire. You haven't seen one, and yet you believe in them. That's called "faith", not evidences, and it is a blind faith at that.
But jinns are older than the Muhammad's Qur'an, in which the pagan Arabs believed in. So why do pagan mythological beings exist in the Qur'an, that supposedly dismiss all pagan superstitions.
You say that Satan Claus and Christmas are pagan beliefs, that Christians have added to their folklore.
But aren't you being a hypocrite, when you accept the pre-Islamic pagan fairytale of jinns?
You are doing exactly the same things as Christians have done. You have incorporated pagan myths into your so-called "holy book".
You cannot kick Christianity as being a pagan knock-off, when Muhammad did the same things with talking animals and non-existent mythical beings, such as angels and jinns.
You have also brought up the Hadeeth, as some of these are authentic and some are not. Based on what? Your logic?
I am afraid when it come to logic, lot of Muslims are not good at logic, especially when dealing with a chapter on Muhammad's night journey to the "Furthest Mosque", which supposedly said to be temple of Jerusalem, which don't exist except they are in ruins at Muhammad's time.
That's over 1200 km away!
How does Muhammad get there?
The Qur'an 17 doesn't say, but according to one of the Hadeeth, which it elaborated, saying Muhammad flew there on a flying winged horse, called Buraq.
Another myth, in Islam. No evidences required, but a lot of blind faith are necessary.
You shouldn't criticise the Bible or Christian teachings, unless you can accept criticism on your own Qur'an, your Messenger and your religion, for spinning distorting fables and myths.