tefilla - Why does the congregation interrupt the chazzan in the middle of sentences of Kaddish?

At one or two points in "Kaddish", the congregation interrupts the chazzan in the middle of a sentence:

Chazzan: יִתְגַּדַּל וְיִתְקַדַּשׁ שְׁמֵהּ רַבָּא / May His great name be exalted and sanctified

Congregation: !אָמֵן / Amen!

Chazzan: בְּעָלְמָא דִּי בְרָא כִרְעוּתֵהּ / in the world which He created according to His will.

and

Chazzan: יִתְבָּרַךְ וְיִשְׁתַּבַּח וְיִתְפָּאַר וְיִתְרומַם וְיִתְנַשּא וְיִתְהַדָּר וְיִתְעַלֶּה וְיִתְהַלָּל שְׁמֵהּ דְּקֻדְשָׁא בְּרִיךְ הוּא / Blessed and praised, glorified and exalted, extolled and honoured, adored and lauded be the name of the Holy One, blessed be He,

Congregation (Some traditions): !בְּרִיךְ הוּא / Blessed be He!

Congregation (Some traditions): !אָמֵן / Amen!

לְעֵלָּא מִן כָּל בִּרְכָתָא וְשִׁירָתָא תֻּשְׁבְּחָתָא וְנֶחֱמָתָא דַּאֲמִירָן בְּעָלְמָא / above and beyond all the blessings, hymns, praises and consolations that are uttered in the world.

^{Translations from Wikipedia}

It seems strange to me to interject these responses in the middle of a sentence, instead of or in addition to at the end of the sentence. Most of the time, when we say "Amen," it's at the end of a blessing.

Why do we interrupt like this in Kaddish?